The inequality given is $x + 4 \leq 10$. Let's analyze this inequality to see which situation matches it best.

First, we solve the inequality:

$x + 4 \leq 10$

Subtract 4 from both sides:

$x \leq 6$

This inequality means that $x$, representing some quantity, must be less than or equal to 6.

Now, let’s evaluate the situations:

A. "Thomas uses $4$ dollars a day to use the fast lane. Determine $x$, the most number of days he can travel and use no more than $10$ dollars."

This suggests we are looking for the number of days, $x$, Thomas can travel, with a total expenditure that does not exceed $10$ dollars. Each day costs $4$ dollars, but here $x + 4 \leq 10$, which doesn't fit perfectly.

B. "Thomas was given $10$ dollars and used $4$ dollars to purchase a book at the school book fair. Determine $x$, the money he has left."

This doesn’t fit because $x$ would represent how much money is left after spending, and the inequality describes a comparison, not a leftover amount.

C. "Thomas walks $4$ miles for $10$ days. Determine $x$, the number of total miles he walked over the $4$-day period."

This is about total miles walked, which doesn't fit the form of the inequality either.

D. "Thomas has a maximum of $10$ dollars to spend this weekend. He spent $x$ dollars on candy and purchased a shirt for $4$ dollars. Determine $x$, the dollars spent on candy."

This situation fits best because it describes the total amount Thomas has to spend ($10$ dollars), the fixed amount spent on the shirt ($4$ dollars), and $x$ dollars spent on candy. This corresponds to $x + 4 \leq 10$, where $x$ represents the amount spent on candy and must be less than or equal to 6.

Answer: The correct situation is D.

Would you like a further explanation or have any questions?

Here are 5 related questions:

1. How do you solve inequalities with more complex expressions?
2. What happens if the inequality was $x + 4 < 10$?
3. Can you create an inequality for a situation where Thomas has $15$ dollars and spends $x$ on lunch and $3$ dollars on a drink?
4. How would you graph the inequality $x + 4 \leq 10$?
5. What are some real-life applications of inequalities?

Tip: Always check which variable the problem is focusing on and what the inequality represents before solving!